Chapter 2 : Structure of Atom
Electron, proton and neutron are sub-atomic particles.
Topics covered in this snack-sized chapter:
In 1850, Faraday began to study electrical discharge in partially evacuated tubes, known as cathode ray discharge tubes.
A cathode ray tube is made of glass containing two thin pieces of metal, called electrodes, sealed in it.
The electrical discharge through the gases could be observed only at very low pressures and at very high voltages. The pressure of different gases could be adjusted by evacuation.
When sufficiently high voltage is applied across the electrodes, current starts flowing through a stream of particles moving in the tube from the negative electrode (cathode) to the positive electrode (anode). These were called cathode rays or cathode ray particles.
The flow of current from cathode to anode was further checked by making a hole in the anode and coating the tube behind anode with phosphorescent material zinc sulphide. When these rays, after passing through anode, strike the zinc sulphide coating, a bright spot on the coating is developed.
2.1.1 Discovery of Electron
Results of the Experiment
The results of these experiments are summarized below.
The cathode rays start from cathode and move towards the anode.
These rays themselves are not visible but their behavior can be observed with the help of certain kind of materials (fluorescent or phosphorescent) which glow when hit by them.
In the absence of electrical or magnetic field, these rays travel in straight lines
J.J. Thomson measured the ratio of electrical charge (e) to the mass of electron (me
) by using cathode ray tube.
Thomson was able to determine the value of e/me
2.1.2 Charge to Mass Ratio of Electron
is the mass of the electron in kg and e is the magnitude of the charge on the electron in coulomb (C).
R.A. Millikan devised a method known as oil drop experiment, to determine the charge on the electrons. He found that the charge on the electron to be – 1.6 × 10–19
The present accepted value of electrical charge is – 1.6022 × 10–19
2.1.3 Charge on the Electron
2.1.4 Discovery of Protons and Neutrons
Electrical discharge carried out in the modified cathode ray tube led to the discovery of particles carrying positive charge.
The smallest and lightest positive ion was obtained from hydrogen and was called proton.
Chadwick bombarded a thin sheet of beryllium by .
When electrically neutral particles having a mass slightly greater than that of the protons was emitted.
He named these particles as neutrons.
An atomic model is a model such that the complete type of every tuple is axiomatized by a single formula. Such types are called principal types, and the formulas that axiomatize them are called complete formulas.
Also known as Plum Pudding Model.
It can be visualised as a pudding or watermelon of positive charge with plums or seeds (electrons) embedded into it.
2.2.1 Thomson Model of Atom
2.2.2 Rutherford’s Nuclear Model of Atom
A stream of high energy from a radioactive source was directed at a thin foil (thickness ) of gold metal.
The thin gold foil had a circular fluorescent zinc sulphide screen around it. Whenever α–particles struck the screen, a tiny flash of light was produced at that point. It was observed that:
- Most of the passed through the gold foil undeflected.
- A small fraction of the was deflected by small angles.
- A very few (1 in 20,000) bounced back, that is, were deflected by nearly 180°.
On the basis of above observations and conclusions, Rutherford proposed the nuclear model of atom (after the discovery of protons). According to this model:
- The positive charge and most of the mass of the atom was densely concentrated in extremely small region. This very small portion of the atom was called nucleus by Rutherford.
- The nucleus is surrounded by electrons that move around the nucleus with a very high speed in circular paths called orbits. Thus, Rutherford’s model of atom resembles the solar system in which the nucleus plays the role of sun and the electrons that of revolving planets.
- Electrons and the nucleus are held together by electrostatic forces of attraction.
2.2.3 Atomic Number and Mass Number
The presence of positive charge on the nucleus is due to the protons in the nucleus.
The number of protons present in the nucleus is equal to atomic number (Z).
For example, the number of protons in the hydrogen nucleus is 1, in sodium atom it is 11.
The mass of the nucleus, due to protons and neutrons.
Protons and neutrons present in the nucleus are collectively known as nucleons.
The total number of nucleons is termed as mass number (A) of the atom.
Mass number (A) = Number of protons (Z
) + Number of neutrons (n)
2.2.4 Isobars and Isotopes
Isobars are the atoms with same mass number but different atomic number for example, and.
Atoms with identical atomic number but different atomic mass number are known as Isotopes.
For example, Protium and Deuterium .
Rutherford model cannot explain the stability of an atom.
It says nothing about the electronic structure of atoms i.e., how the electrons are distributed around the nucleus and what are the energies of these electrons.
2.2.5 Drawbacks of Rutherford’s Model
Dual character of the electromagnetic radiation which means that radiations possess both wave like and particle like properties, and
Experimental results regarding atomic spectra which can be explained only by assuming quantized electronic energy levels in atoms.
2.3 DEVELOPMENTS LEADING TO THE BOHR’S MODEL OF ATOM arrow_upward
Maxwell suggested that when electrically charged particle moves under acceleration, alternating electrical and magnetic fields are produced and transmitted.
These fields are transmitted in the forms of waves called electromagnetic waves or electromagnetic radiation.
2.3.1 Wave Nature of Electromagnetic Radiation
The oscillating electric and magnetic fields produced by oscillating charged particles are perpendicular to each other and both are perpendicular to the direction of propagation of the wave.
Unlike sound waves or water waves, electromagnetic waves do not require medium and can move in vacuum.
There are many types of electromagnetic radiations, which differ from one another in wavelength (or frequency). These constitute what is called electromagnetic spectrum.
Different kinds of units are used to represent electromagnetic radiation.
These radiations are characterized by the properties, namely, frequency and wavelength.
Planck suggested that atoms and molecules could emit (or absorb) energy only in discrete quantities and not in a continuous manner, a belief popular at that time.
Planck gave the name quantum to the smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation.
2.3.2 Particle Nature of Electromagnetic Radiation: Planck’s Quantum Theory
The energy (E) of a quantum of radiation is proportional to its frequency and is expressed by the following equation
The proportionality constant, ‘h’ is known as Planck’s constant and has the value 6.626 × 10–34
With this theory, Planck was able to explain the distribution of intensity in the radiation from black body as a function of frequency or wavelength at different temperatures.
Hertz performed a very interesting experiment in which electrons (or electric current) were ejected when certain metals (for example potassium, rubidium, caesium etc.) were exposed to a beam of light.
This phenomenon is known as Photoelectric effect.
The results observed in this experiment were:
The electrons are ejected from the metal surface as soon as the beam of light strikes the surface, i.e., there is no time lag between the striking of light beam and the ejection of electrons from the metal surface.
The number of electrons ejected is proportional to the intensity or brightness of light.
For each metal, there is a characteristic minimum frequency, (also known as threshold frequency) below which photoelectric effect is not observed. At a frequency, the ejected electrons come out with certain kinetic energy. The kinetic energies of these electrons increase with the increase of frequency of the light used.
Photon a particle representing a quantum of light or other electromagnetic radiation.
When a photon of sufficient energy strikes an electron in the atom of the metal, it transfers its energy instantaneously to the electron during the collision and the electron is ejected without any time lag or delay.
Greater the energy possessed by the photon, greater will be transfer of energy to the electron and greater the kinetic energy of the ejected electron.
In other words, kinetic energy of the ejected electron is proportional to the frequency of the electromagnetic radiation.
Since the striking photon has energy equal to and the minimum energy required to eject the electron is, then the difference in energy is transferred as the kinetic energy of the photoelectron.
Following the conservation of energy principle, the kinetic energy of the ejected electron is given by the equation:
is the mass of the electron and v is the velocity associated with ejected electron.
Light has dual behaviour. Depending on the experiment, we find that light behaves either as a wave or as a stream of particles.
Whenever radiation interacts with matter, it displays particle like properties in contrast to the wavelike properties (interference and diffraction), which it exhibits when it propagates.
The spectrum of radiation emitted by a substance that has absorbed energy is called an emission spectrum. Atoms, molecules or ions that have absorbed radiation are said to be “excited”.
An absorption spectrum is like the photographic negative of an emission spectrum.
Dual Behavior of Electromagnetic Radiation
The study of emission or absorption spectra is referred to as spectroscopy.
The spectrum of the visible light, was continuous as all wavelengths (red to violet) of the visible light are represented in the spectra.
The emission spectra of atoms in the gas phase, do not show a continuous spread of wavelength from red to violet, rather they emit light only at specific wavelengths with dark spaces between them. Such spectra are called line spectra or atomic spectra because the emitted radiation is identified by the appearance of bright lines in the spectra.
When an electric discharge is passed through gaseous hydrogen, the H2
molecules dissociate and the energetically excited hydrogen atoms produced emit electromagnetic radiation of discrete frequencies. The hydrogen spectrum consists of several series of lines named after their discoverers.
Line Spectrum of Hydrogen
Balmer showed on the basis of experimental observations that if spectral lines are expressed in terms of wavenumber , then the visible lines of the hydrogen spectrum obey the following formula:
Where n is an integer equal to or greater than 3.
The series of lines described by this formula are called the Balmer series.
The Balmer series of lines are the only lines in the hydrogen spectrum which appear in the visible region of the electromagnetic spectrum.
Rydberg, noted that all series of lines in the hydrogen spectrum could be described by the following expression:
The value 109,677 cm–1
is called the Rydberg constant for hydrogen.
The speed of light depends upon the nature of the medium through which it passes.
The beam of light is deviated or refracted from its original path as it passes from one medium to another.
When a ray of white light is passed through a prism, the wave with shorter wavelength bends more than the one with a longer wavelength.
Bohr’s model for hydrogen atom is based on the following postulates:
2.3.3 Evidence for the Quantized Electronic Energy Levels: Atomic Spectra
- The electron in the hydrogen atom can move around the nucleus in a circular path of fixed radius and energy. These paths are called orbits, stationary states or allowed energy states. These orbits are arranged concentrically around the nucleus.
- The energy of an electron in the orbit does not change with time. However the electron will move from a lower stationary state to a higher stationary state when required amount of energy is absorbed by the electron or energy is emitted when electron moves from higher stationary state to lower stationary state.
- The frequency of radiation absorbed or emitted when transition occurs between two stationary states that differ in energy by , is given by :
- The angular momentum of an electron in a given stationary state can be expressed as:
According to Bohr’s theory for hydrogen atom:
- The stationary states for electron are numbered n = 1, 2, 3.......... These integral numbers are known as Principal quantum numbers.
- The radii of the stationary states are expressed as:
- Where a0
= 52.9 pm. Thus the radius of the first stationary state, called the Bohr orbit, is 52.9 pm. normally the electron in the hydrogen atom is found in this orbit (that is n=1). As n increases the value of r will increase. In other words the electron will be present away from the nucleus.
- The most important property associated with the electron, is the energy of its stationary state. It is given by the expression.
- Where RH
is called Rydberg constant and its value is 2.18 × 10-18
- The energy of the lowest state also called the ground state is:
- The energy of the stationary state for n = 2 will be:
- Bohr’s theory can also be applied to the ions containing only one electron, similar to that present in hydrogen atom. For example, He+
etc. The energies of the stationary states associated with these kinds of ions are given by the expression.
When an electric discharge is passed through gaseous hydrogen, the H2
molecules dissociate and the energetically excited hydrogen atoms produced emit electromagnetic radiation of discrete frequencies.
2.4.1 Explanation of Line Spectrum of
It fails to account for the finer details (doublet, that is two closely spaced lines) of the hydrogen atom spectrum observed by using sophisticated spectroscopic techniques.
This model is also unable to explain the spectrum of atoms other than hydrogen, for example, helium atom which possesses only two electrons.
Further, Bohr’s theory was also unable to explain the splitting of spectral lines in the presence of magnetic field (Zeeman Effect) or an electric field (Stark effect).
It could not explain the ability of atoms to form molecules by chemical bonds.
De Broglie proposed that matter, like radiation, should also exhibit dual behavior i.e., both particle and wavelike properties.
2.4.2 Limitations of Bohr’s Model
This means that just as the photon has momentum as well as wavelength, electrons should also have momentum as well as wavelength, de Broglie, from this analogy, gave the following relation between wavelength and momentum (p) of a material particle.
Where m is the mass of the particle, v its velocity and p its momentum.
De Broglie’s prediction was confirmed experimentally when it was found that an electron beam undergoes diffraction, a phenomenon characteristic of waves.
It states that it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron.
Mathematically, it can be given as in equation:
Where is the uncertainty in position, (or ) is the uncertainty in momentum (or velocity) of the particle.
It rules out existence of definite paths or trajectories of electrons and other similar particles.
The effect of Heisenberg Uncertainty Principle is significant only for motion of microscopic objects and is negligible for that of macroscopic objects.
In dealing with milligram-sized or heavier objects, the associated uncertainties are hardly of any real consequence.
The precise statements of the position and momentum of electrons have to be replaced by the statements of probability, that the electron has at a given position and momentum.
Significance of Uncertainty Principle
The branch of science that takes into account this dual behavior of matter is called quantum mechanics.
Quantum mechanics is a theoretical science that deals with the study of the motions of the microscopic objects that have both observable wave like and particle like properties. It specifies the laws of motion that these objects obey.
The fundamental equation of quantum mechanics was developed by Schrödinger.
The Schrödinger equation is written as:
2.6 Quantum Mechanical Model of Atom
- Where is a mathematical operator called Hamiltonian.
Atomic orbitals are precisely distinguished by quantum numbers.
Each orbital is designated by three quantum numbers labelled as n, l and ml
2.6.1 Orbitals and Quantum Numbers
Principal Quantum Number (n)
The principal quantum number ‘n’ is a positive integer with value of n = 1, 2, 3....... .
The principal quantum number determines the size and to large extent the energy of the orbital.
The principal quantum number also identifies the shell. With the increase in the value of ‘n’, the number of allowed orbital increases and are given by ‘n2
All the orbitals of a given value of ‘n’ constitute a single shell of atom and are represented by the following letters